pith. sign in
theorem

prime_threehundredfiftythree

proved
show as:
module
IndisputableMonolith.NumberTheory.Primes.ArithmeticFunctions
domain
NumberTheory
line
2009 · github
papers citing
none yet

plain-language theorem explainer

353 is established as a prime number. Number theorists applying Möbius function identities to small integers would cite this fact when verifying squarefree cases or inversion formulas. The proof is a one-line native decision that resolves the primality predicate by direct computation.

Claim. The natural number 353 is prime.

background

The module supplies lightweight wrappers around Mathlib arithmetic functions, beginning with the Möbius function μ. Prime is the transparent alias for the standard Nat.Prime predicate on natural numbers. Upstream results include the basic Prime definition together with structural assertions from foundational modules on collision-free programs and simplicial structures, though none alter the primality check itself.

proof idea

The proof is a one-line wrapper that applies native_decide to discharge the primality statement by computational verification.

why it matters

The declaration supplies a verified small-prime instance inside the arithmetic-functions module, supporting later Möbius statements such as mobius_prime. It fills a concrete number-theoretic foothold but does not invoke Recognition Science landmarks such as the J-uniqueness map, the phi-ladder, or the eight-tick octave. No downstream uses are recorded.

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